Spinors and mass on weighted manifolds
Abstract This paper generalizes classical spin geometry to the setting of weighted manifolds (manifolds with density) and provides applications to the Ricci flow. Spectral properties of the naturally associated weighted Dirac operator, introduced by Perelman, and its relationship with t...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Springer Berlin Heidelberg
2022
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| Online Access: | https://hdl.handle.net/1721.1/143643 |
| _version_ | 1826202993773510656 |
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| author | Baldauf, Julius Ozuch, Tristan |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Baldauf, Julius Ozuch, Tristan |
| author_sort | Baldauf, Julius |
| collection | MIT |
| description | Abstract
This paper generalizes classical spin geometry to the setting of weighted manifolds (manifolds with density) and provides applications to the Ricci flow. Spectral properties of the naturally associated weighted Dirac operator, introduced by Perelman, and its relationship with the weighted scalar curvature are investigated. Further, a generalization of the ADM mass for weighted asymptotically Euclidean (AE) manifolds is defined; on manifolds with nonnegative weighted scalar curvature, it satisfies a weighted Witten formula and thereby a positive weighted mass theorem. Finally, on such manifolds, Ricci flow is the gradient flow of said weighted ADM mass, for a natural choice of weight function. This yields a monotonicity formula for the weighted spinorial Dirichlet energy of a weighted Witten spinor along Ricci flow. |
| first_indexed | 2024-09-23T12:29:29Z |
| format | Article |
| id | mit-1721.1/143643 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T12:29:29Z |
| publishDate | 2022 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1436432023-02-14T19:25:26Z Spinors and mass on weighted manifolds Baldauf, Julius Ozuch, Tristan Massachusetts Institute of Technology. Department of Mathematics Abstract This paper generalizes classical spin geometry to the setting of weighted manifolds (manifolds with density) and provides applications to the Ricci flow. Spectral properties of the naturally associated weighted Dirac operator, introduced by Perelman, and its relationship with the weighted scalar curvature are investigated. Further, a generalization of the ADM mass for weighted asymptotically Euclidean (AE) manifolds is defined; on manifolds with nonnegative weighted scalar curvature, it satisfies a weighted Witten formula and thereby a positive weighted mass theorem. Finally, on such manifolds, Ricci flow is the gradient flow of said weighted ADM mass, for a natural choice of weight function. This yields a monotonicity formula for the weighted spinorial Dirichlet energy of a weighted Witten spinor along Ricci flow. 2022-07-11T15:23:55Z 2022-07-11T15:23:55Z 2022-07-07 2022-07-10T03:21:37Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/143643 Baldauf, Julius and Ozuch, Tristan. 2022. "Spinors and mass on weighted manifolds." PUBLISHER_CC en https://doi.org/10.1007/s00220-022-04420-y Creative Commons Attribution https://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Baldauf, Julius Ozuch, Tristan Spinors and mass on weighted manifolds |
| title | Spinors and mass on weighted manifolds |
| title_full | Spinors and mass on weighted manifolds |
| title_fullStr | Spinors and mass on weighted manifolds |
| title_full_unstemmed | Spinors and mass on weighted manifolds |
| title_short | Spinors and mass on weighted manifolds |
| title_sort | spinors and mass on weighted manifolds |
| url | https://hdl.handle.net/1721.1/143643 |
| work_keys_str_mv | AT baldaufjulius spinorsandmassonweightedmanifolds AT ozuchtristan spinorsandmassonweightedmanifolds |